The truce is to lead to a new border deal for Gaza, with Egypt hosting indirect talks between Israel and Hamas. Israel has shunned Hamas as a terrorist group and refuses to negotiate with it directly.
After the Hamas takeover in 2007, Israel and then-Egyptian President Hosni Mubarak sealed Gaza to isolate the Islamic militants and make it harder for them to govern.
The restrictions have since been eased because of international pressure on Israel and because of regime change in Egypt. Both Hamas and Egyptian President Mohammed Morsi, elected earlier this year, are members of the region-wide Muslim Brotherhood movement.
Before the Nov. 14 start of the fighting, Gaza received most of its consumer goods through an Israeli cargo crossing, while Israel banned virtually all exports and travel from Gaza, preventing the area's battered economy from bouncing back.
Items restricted by Israel, such as construction materials, were brought into Gaza through smuggling tunnels from Egypt, along with weapons for Hamas.
Israel also restricted the movement of Gaza's fishermen and farmers in border areas, citing security concerns.
On Saturday, fishermen were able to sail six nautical miles out to sea, or double the previous limit, said Mahfouz Kabariti, head of the local fishermen's association. He said several fishermen already made the journey Saturday.
"This is an opportunity and a chance for a better catch, though it is still a limited area," said Kabariti, who represents some 3,500 fishermen.
Israeli navy boats have been enforcing a sea blockade in an attempt to prevent weapons smuggling to Gaza. The restrictions on fishermen have fluctuated over the years, linked to the ups and downs in Israeli-Palestinian relations.
Meanwhile, some Gaza residents said they were able to enter an Israeli-enforced buffer zone on the Gaza side of the border Saturday with Israel without fear of being fired on.
Israel's military carved out a 300-meter-wide (300-yard-wide) zone several years to try to prevent militants from sneaking into Israel. The zone gobbled up scarce acres of farmland in one of the most densely populated areas in the world.
On Friday, hundreds of Palestinians surged toward the border fence, but Israeli soldiers fired to push them back, killing one man and wounding at least 19 people.
On Saturday, 42-year-old farmer Nidal Abu Dakka said soldiers stood and watched as he and others moved close to the fence. Abu Dakka, speaking by phone, said he was inspecting his land, some 60 meters from the border, and planned to plant wheat and barley soon.
In other border areas, residents said Hamas police kept them away from the fence.
An Israeli government spokesman said he was unaware restrictions had been eased. A defense official said the Israeli military was no longer enforcing the no-go zone, but reserved the right to act against suspicious people. Both spoke on condition of anonymity because they were not allowed to discuss the issue with reporters.